Mathematicians Just Found A New Prime Number — With 17 Million Digits

An Internet search team looking for ever more prime numbers has
broken their four-year dry spell and just announced that they
found a new one — with 17 million digits. I can't write out those
digits for you, but here's the short hand: 2 ^ 57,885,161 minus
1.

For those not in the math know, a prime number is a special kind
of number that can only be divided by itself and one. The search
party, called the Great
Internet Mersenne Prime Search, is actually searching for an
even more unique number — a special kind of prime number called a
Mersenne prime, a prime number that can be written in scientific
shorthand 2p - 1, where the exponent is
itself a prime. In this example, 57,885,161 is the prime
exponent.

This new number is only the 48th Mersenne prime ever found. It's
also the biggest. The second largest Mersenne prime has just
under 13 million digits. Here's how they do it, explained by
Jacob Aron of New Scientist:

Though there are an infinite number of primes, there is no
formula for generating these numbers, so discovering them
requires intensive computation. GIMPS uses volunteers' computers
to sift through each prime-number candidate in turn, until
eventually one lucky user discovers a new prime.

... Though there is little mathematical value to finding a single
new prime, these rare numbers are prized in their own right by
some. "It's sort of like finding a diamond," says Chris Caldwell
at the University of Tennessee, Martin, who keeps a record of the
largest known primes. "For some reason people decide they like
diamonds and so they have a value. People like these large primes
and so they also have a value."

After the discovery, it took 39 days of calculations to prove the
number was a Mersenne prime.

Prime numbers are also important in cryptography, which is used
to make online transactions secure.